To provide references for the IRS diagnosis, we refer to extensive related works on antenna array diagnosis.
Early representative works include [1]} and [2]}.
These techniques exploit the linear relationship between antenna pattern and array excitation, and take samples uniformly on the radiation pattern to recover actual array excitation by solving an inverse problem.
Therefore, faulty antenna elements can be identified by comparing the actual array excitation and the ideal one.
In order to make the inverse problem solvable, these techniques require the number of measurements no less than the total number of antenna elements, which may be time-consuming for large-scale systems.
About a decade ago, compressed sensing was introduced to array diagnosis [3]}, which efficiently captures the failure sparsity that the number of faulty antenna elements is usually much smaller than the total number of antenna elements.
Hence, one can subtract the ideal antenna pattern from the observed one to obtain the differential pattern.
The resulting differential array excitation is a sparse signal that can be recovered from compressed measurements, in which non-zero entries indicate faulty antenna elements.
That work has initiated numerous compressed sensing based diagnostic techniques.
One type of improvement focuses on the enhancement in sparse recovery algorithms, such as Bayesian compressive sensing [4]}, [5]}, non-convex compressed sensing [6]}, and mixed-norm constrained compressed sensing [7]}.
Other improvements are mainly the development of new sampling methods, including far-field sampling [8]}, phase-less sampling [9]}, phase domain sampling [10]}, and random beam sampling [11]}, [12]}, [13]}.
In particular, the work [14]} extended the above antenna-only diagnoses to the joint diagnosis of antenna, phase shifter, and RF chain of hybrid beamforming (HBF) system.
